Researchers used two footballs of the same size to examine the effect of helium on kicking distance. One football was filled with air, and the other was filled with helium. Eleven people participated in the study. Each person kicked the football filled with air and the football filled with helium, and the kicking distances, in yards, were recorded. The football that was kicked first was determined by the flip of a fair coin, and the people did not know which football was filled with air and which was filled with helium. What type of study was conducted by the researchers and, of the following, which is the appropriate t- interval for inference? (A)A completely randomized design and a t-interval for a difference between means for independent samples (B)A completely randomized design and a t-interval for a mean difference (C)A matched-pairs design and a t-interval for a difference between means for independent samples (D)A matched-pairs design and a -interval for a mean difference (E) An observational study and a t-interval for a difference between means for independent samples

The true statements are:

From the question, we understand that:

The above highlights mean that:

The type of study is a matched-pair design

And as such, the appropriate t- interval is a t-interval for a difference between means for independent samples

Hence, option (c) is correct

Read more about matched pair designs at:

link

(C)A matched-pairs design and a t-interval for a difference between means for independent samples.

Step-by-step explanation:

A matched-pairs design is a design technique that is used by researchers to compare two similar variables (objects or people).

In matched-pairs design, the two variables are splitted(divided into two) , one variable is placed in the treatment group and the other is placed in a control group.

Matched-pairs design is a design that helps to minimise and prevent the interference of external variables in the experiment.

In the question above, the experiment in the question utilises the used of a matched-pair design because we are comparing two similar objects together with is two footballs of similar size but one contains air while the other one contains helium.

The t-interval for inference used in this experiment(matched-pairs design) is a t-interval for a difference between means for independent samples.

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step-by-step explanation: